A hand saw has a reputation for being hard, but most beginner cuts go wrong for one reason: pushing too hard. The saw is designed to cut on its own weight, so how you hold it and where you start matter more than strength.
Your first day
You'll need a crosscut hand saw, a scrap board about a foot long, a clamp, sandpaper, safety glasses, a dust mask, a pencil and a ruler, well under fifty dollars if you buy secondhand. Put on the glasses, and the mask for the sanding. Clamp the board to a stable surface so it can't shift mid-cut, and keep your off-hand well clear of the saw's path. Mark a straight line with a pencil and straightedge.
Place the hand saw on the waste side of the line, the side you're throwing away, and start with a few slow backward strokes to create a groove. Then saw forward and back in long, even strokes with the blade at roughly 45 degrees to the board, letting the saw's own weight do most of the work. Slow right down for the last few strokes so the offcut doesn't tear a splinter off the board or pinch the blade.
Sand the cut edge with 120-grit paper until it's smooth to the touch.
Most beginners push down hard on the saw to force it through faster. Don't. It actually makes the cut wander off the line more, not less. Let the saw's weight and a consistent angle do the cutting instead of arm strength.
The thing most people miss
It's easy to believe clean results need expensive power tools, and that a hand saw is what you settle for until you can afford better. In practice a hand saw used slowly and correctly can cut a cleaner line than a power saw used in a rush, because a straight cut comes from a steady angle and a marked line you follow, not from motor power.
Better tools don't fix bad technique, they make it faster. Learning the technique on a cheap saw first means it carries over when you do use power tools.
What not to buy
Don't buy a set of chisels, planes and extra clamps before this first cut. One saw, a pencil, a straightedge and sandpaper are all this exercise needs, and a bigger toolkit just gives you more ways to skip the practice.
Check your cut by holding a straightedge against it: any gap you can see is where the saw wandered. Repeat the cut a few times and the line gets straighter as your stroke settles. Basic joinery, starting with a butt joint, one board's end glued flat against the face of another, is the natural next thing to try.